Are state- and time- dependent models really different?

Yes, state- and time-dependent models are really different, but only for large monetary shocks. In particular, we show that in a broad class of models where shocks have continuous paths, the propagation of a monetary impulse is independent of the nature of the sticky price friction when shocks are small. The propagation of large shocks instead depends on the nature of the friction: the impulse response of inflation to monetary shocks is independent of the shock size in time-dependent models, while it is nonlinear in state-dependent models. We use data on exchange rate devaluations and inflation for a panel of countries froM1974 to 2014 to test for the presence of state-dependent decision rules. We present some evidence of a nonlinear effect of exchange rate changes on prices in a sample of flexible exchange rate countries withlow inflation. We discuss the dimensions in whichthis finding is robust and the ones in whichit is not.